1) Chibi-Usa's best friends are all quiet, serious people. Hotaru. Setsuna. Pegasus (he's REALLY mysterious).
2) Taiki...I'm not sure, but I couldn't see her not liking Chibi-Usa. And, yes, Chibi-Usa is popular on the show itself...it says she makes a lot of friends at school, not to mention winning the hearts of the other Senshi.
3) Chibi-Usa also does well in school like Taiki. You never see her coming home with bad grades (in the second episode of SuperS, she and Shingo came home with 100 percents on their tests). She at least gets better grades than her mom.
4) The fact that Taiki is an alien who changes genders wouldn't freak out Chibi-Usa, because she befriends those who have "freaky" traits anyway (like how she was the first person to like Hotaru's healing power).
5) They have had similar experiences, too. Chibi-Usa has experienced the destruction of Crystal Tokyo, as well as being separated from everything she loves to accomplish a mission (she's looking for the Silver Crystal in R). People often point to the Starlights feeling a bit guilty about what happened to their planet and being depressed a lot (especially Taiki). In R, at least, Chibi-Usa is a very depressed little girl too. She KNOWS she's caused at least part of the destruction of Crystal Tokyo by losing the future Silver Crystal. So don't be too quick to assume that Chibi-Usa is too bright and cheerful for Taiki. Later on, she probably still remembers her experiences, which might be why she seemed to empathize with Hotaru so much.
6) Age wouldn't be a problem--she's friends with Setsuna, who is ageless!
And yes, I do know that Chibi-Usa and Taiki live in different times as well as different planets, so even if they were to meet and have a friendship, it would be a tragic one. But I still support this friendship pairing.